Chapter 10.6, Problem 17E

Fish Population with Harvesting The fish population in a pond with carrying capacity $1000$ is modeled by the logistic equation

$\frac{dN}{dt}=\frac{.4}{1000}N\left(1000-N\right)$.

Here, $N(t)$ denotes the number of fish at time $t$ in years. When the number of fish reached $275$, the owner of the pond decided to remove $75$ fish per year.

a) Modify the differential equation to model the population of fish from the time it reached $275$.

b) Plot several solution curves of the new equation, including the solution curve with $N(0)=275$.

c) Is the practice of catching $75$ fish per year sustainable, or will it deplete the fish population in the pond? Will the size of the fish population ever come close to the carrying capacity of the pond?